The equation of the function g(x) is g(x) = x - 1
<h3>How to determine the
equation of the
function g(x)?</h3>
The given parameters are:
f(x) = x - 5
The above function f(x) is translated left by 4 units
So, we have
g(x) = f(x + 4)
This gives
f(x + 4) = x + 4- 5
Evaluate the sum
f(x + 4) = x - 1
So, we have:
g(x) = x - 1
Hence, the equation of the function g(x) is g(x) = x - 1
Read more about function transformation at:
brainly.com/question/10904859
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Let P(a, b) be a point on the coordinate plane. Then the following hold:
i) If a>0, b>0 then P is in the I.Quadrant.
ii) If a<0, b>0 then P is in the II.Quadrant.
iii) If a<0, b<0 then P is in the III.Quadrant.
iv) If a>0, b<0 then P is in the IV.Quadrant.
v) If a=0 and b is positive or negative, then P is on the y-axis.
vi) If b=0 and a is positive or negative, then P is on the x-axis.
Since we have: a=0, and 19 positive, then this point is on the y-axis.
Answer: y-axis
The midpoint of these two points is (-1, 8).
In order to find the midpoint, you must take the average of each part of the coordinates. You do this by adding them together and dividing by 2. We'll start with the x-coordinates.
(-1 + -1)/2 = -1
Now we'll use the y-coordinates.
(10 + 6)/2 = 8
This gives us the ordered pair of (-1, 8)
The answer, in short, is that the short leg equals 15 mm, the long leg equals 20 mm, and the hypotenuse equals 25mm. but if you'd like to see how I solved it, here are the steps.
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The Pythagorean theorem (also known as Pythagoras's Theorem) can be used to solve this. This theorem states that one leg or a right triangle squared plus the other side of that same triangle squared equals the hypotenuse of that triangle squared. To put it in equation form, L² + L² = H².
Let's call the longer leg B, the shorter leg A, and the hypotenuse H.
From the question, we know that A = B - 5, and H = B + 5.
So if we put those values into an equation, we have (B - 5)² + B² = (B + 5)²
Now, to solve. Let's square the two terms in parentheses first:
(B² - 5B - 5B + 25) + B² = B² + 5B + 5B + 25
Now combine like terms:
2B² -10B + 25 = B² + 10B + 25
And now we simplify. Subtract 25 from each side:
2B² - 10B = B² + 10B
Subtract B² from each side:
B² - 10B = 10B
Add 10B to each side:
B² = 20B
And finally, divide each side by B:
B = 20
So that's the length of B. Now to find out A and H.
A = B - 5, so A = 15.
H = B + 5, so H = 25.
And your final answer is A = 15mm, B = 20mm, and H = 25mm
